問28
頻出度★☆☆
リアルタイムで画像処理を行うシステムを開発するために, 必要となるCPU単一の性能を調べたところ, 現在販売されているCPUの32倍の性能が必要であることが分かった。販売されるCPUの性能が2年ごとに倍増するとしたとき, このシステムに必要なCPUが販売されるのは何年後か。
平成29年度 春期 ITパスポート試験 問28
テクノロジ系コンピュータ構成要素 › プロセッサ
This question's explanation and your answers so far.
解説
問 28
Incorrectア
After 6 years there are only 3 doublings (2 years × 3), so performance reaches only 2 to the 3rd power = 8 times, which falls short of the required 32 times, so it is incorrect.
- イ
正解 The required performance is 32 times that of the current CPU. CPU performance doubles every 2 years. Expressing 32 as a power of 2 gives 32 = 2 to the 5th power, so making performance 32 times greater requires doubling 5 times. Since each doubling takes 2 years, 2 years × 5 = 10 years, after which a CPU with exactly 32 times the performance goes on sale. Therefore the correct answer is “イ”, 10 years later. The doubling progression can be confirmed as: after 2 years 2 times, after 4 years 4 times, after 6 years 8 times, after 8 years 16 times, and after 10 years 32 times.
Incorrectウ
After 16 years there are 8 doublings, so performance becomes 2 to the 8th power = 256 times, far exceeding the required 32 times. Since the question asks for the shortest number of years to reach 32 times, it is incorrect.
Incorrectエ
This confuses the required multiple “32 times” with the number of years in the answer. What is actually needed is the 10 years corresponding to 5 doublings; after 32 years there would be 16 doublings = 2 to the 16th power times, an unrealistically high level of performance, so it is incorrect.
ここがポイント
- A quantity that doubles every fixed period grows exponentially. Express the required multiple as a power of 2 (32 = 2 to the 5th power), then multiply the exponent (= the number of doublings) by the length of one period to find the required number of years.
- This reflects the idea, represented by “Moore's law”, that semiconductor performance doubles at a fixed cycle. The key is the calculation that decomposes the multiple into a power of 2.
用語